Question

1. find ( mangle lmn ).

Explanation:

Step1: Set angles equal (congruent triangles)

$4x + 2 = 7x - 37$

Step2: Solve for x (isolate variable)

$2 + 37 = 7x - 4x$
$39 = 3x$
$x = \frac{39}{3} = 13$

Step3: Calculate $m\angle LMN$

$m\angle LMN = (4x + 2)^\circ + (7x - 37)^\circ$
Substitute $x=13$:
$m\angle LMN = (4(13)+2) + (7(13)-37)$
$m\angle LMN = (52+2) + (91-37)$
$m\angle LMN = 54 + 54$

Answer:

$108^\circ$